In mathematics, a set is considered "non-compact" if it does not meet the criteria for compactness. A set is compact if it is both closed and bounded, meaning it contains all its limit points and fits within a finite space. Non-compact sets can extend infinitely or lack closure, making them unable to satisfy these conditions. For example, the set of all real numbers, denoted as ℝ, is non-compact because it stretches infinitely in both directions. Similarly, an open interval like 0, 1 is non-compact since it does not include its endpoints, failing the closed condition.